# Activity 12F: Explaining Why the Area Formula for Triangles is Valid

- Author:
- Erika Bratcher, Trevor Leach

**In Part A, you will use the moving and additivity principles to explain in three ways why the following right triangle has area**

__PART A (RIGHT TRIANGLES) DIRECTIONS:__## Way #1

Explain how the demonstration above shows that the area of a triangle is . Be sure to mention any principles of area helpful to your explanation.

## Way #2

Use the demonstration above to explain why the area of a triangle can also be thought of as . Be sure to mention any principles of area helpful to your explanation.

## Way #3

Use the demonstration above to explain why the area of a triangle can also be thought of as . Be sure to mention any principles of area helpful to your explanation.

__In Part B, you will use the moving and additivity principles to explain in two ways why the acute triangle below has area__

**PART B (ACUTE TRIANGLES) DIRECTIONS:**## Way #1

Use the demonstration above to explain why the area of a triangle can also be thought of as . Be sure to mention any principles of area helpful to your explanation.

## Way #2

**Now, we will apply what we know about right triangles in order to prove the formula for the area of an obtuse triangle is also**

__PART C (OBTUSE TRIANGLES) DIRECTIONS:__Use the figure above AND what you know about right triangle areas to prove that the area of the purple obtuse triangle is also